# The Smeared Null Energy Condition

@article{Freivogel2018TheSN, title={The Smeared Null Energy Condition}, author={Ben Freivogel and Dimitrios Krommydas}, journal={Journal of High Energy Physics}, year={2018}, volume={2018}, pages={1-29} }

A bstractWe propose a new bound on a weighted average of the null energy along a finite portion of a null geodesic: the Smeared Null Energy Condition (SNEC). We believe our bound is valid on scales small compared to the radius of curvature in any quantum field theory that is consistently coupled to gravity. If correct, our bound implies that regions of negative energy density are never strongly gravitating, and that isolated regions of negative energy are forbidden.

## 10 Citations

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## References

SHOWING 1-10 OF 58 REFERENCES

Achronal averaged null energy condition

- Physics
- 2007

The averaged null energy condition (ANEC) requires that the integral over a complete null geodesic of the stress-energy tensor projected onto the geodesic tangent vector is never negative. This…

Holographic proof of the averaged null energy condition

- Physics
- 2014

The averaged null energy conditions (ANEC) states that, along a complete null curve, the negative energy fluctuations of a quantum field must be balanced by positive energy fluctuations. We use the…

Averaged null energy condition and quantum inequalities in curved spacetime

- Physics
- 2015

The Averaged Null Energy Condition (ANEC) states that the integral along a complete null geodesic of the projection of the stress-energy tensor onto the tangent vector to the geodesic cannot be…

Derivation of the null energy condition

- Physics
- 2015

We derive the null energy condition, understood as a constraint on the Einstein-frame Ricci tensor, from world sheet string theory. For a closed bosonic string propagating in a curved geometry, the…

Averaged null energy condition from causality

- Physics
- 2016

A bstractUnitary, Lorentz-invariant quantum field theories in flat spacetime obey mi-crocausality: commutators vanish at spacelike separation. For interacting theories in more than two dimensions, we…

General proof of the averaged null energy condition for a massless scalar field in two-dimensional curved spacetime.

- Physics, MathematicsPhysical review. D, Particles and fields
- 1991

The proof shows that the ANEC is a direct consequence of the general positivity condition which must hold for the two-point function of any state, and extends to establish the AN EC for the null geodesic generators of the horizon (provided that there exists a stationary Hadamard state of the field).

Singularity theorems from weakened energy conditions

- Mathematics, Physics
- 2011

We establish analogues of the Hawking and Penrose singularity theorems based on (a) averaged energy conditions with exponential damping; (b) conditions on local stress–energy averages inspired by the…

Null energy conditions in quantum field theory

- Physics
- 2003

For the quantized, massless, minimally coupled real scalar field in four-dimensional Minkowski space, we show (by an explicit construction) that weighted averages of the null-contracted stress-energy…

Two Roads to the Null Energy Condition

- Physics
- 2015

The null energy condition has sweeping consequences in general relativity. I argue here that it has been misunderstood as a property exclusively of matter, when in fact it arises only in a theory of…

Wormholes supported by phantom-like modified Chaplygin gas

- Physics
- 2008

We have examined the possible construction of a stationary, spherically symmetric and spatially inhomogeneous wormhole spacetime supported by the phantom energy. The latter is supposed to be…